Hey
To answer your question I'll address the order of arpeggios in a major key so you can get those under your fingers as that might fix all your confusion the quickest.
In any major scale, or key, the order of arpeggios is:
maj7 - m7 - m7 - maj7 - 7 - m7 - m7b5
So for the key of E, like you mentioned, the arpeggios would be:
Emaj7 - F#m7 - G#m7 - Amaj7 - B7 - C#m7 - D#m7b5
The m7b5 arpeggio is also referred to as the "half-diminished" arpeggio, but there is no diminished arpeggio in the major arpeggios.
Here's some more info on the m7b5 arpeggio to check out, hope this helps!
http://www.guitarmasterclass.net/guitar_fo...showtopic=48488